The importance and near ubiquity of the Golden Ratio in disciplines like chemistry and biology is well known, but only recently has it come to light in areas pertaining to the Quantum domain. By using a modified tool-kit of hyper-complex numbers (known as Dimensional Gate Operators) and numerical analysis, we uncover a connection between hyper-dimensional objects, the Fibonacci sequence and that of quasiparticles and excitations. The results show that dimensionality increases in step with the Fibonacci sequence.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, exponential generating functions for these numbers. Then we define an associate matrix for these numbers. In addition, using this matrix, we present two different versions of Cassini identitiy of these numbers.

Hydroperoxides (ROOH) are known as damaging agents capable of mediating mutation, while a role as signaling agents through oxidation of protein sulfhydryls that can alter cancer-related pathways has gained traction. Glutathione peroxidase 2 (GPX2) is an antioxidant enzyme that reduces ROOH at the expense of glutathione (GSH). GPX2 is noted for a tendency of large in-creases or decreases in expression levels during tumorigenesis that leads to investigators focusing on its role in cancer. However, GPX2 is only one component of multiple enzyme families that metabolize ROOH and GPX2 levels are often very low in the context of these other ROOH reducing activities. Colorectal cancer (CRC) was selected as a case study for examining GPX2 function as colorectal tissues and cancers are sites where GPX2 is highly expressed. A case can be made for a significant impact of changes in expression levels. There is also a link between GPX2 and NADPH oxidase 1 (NOX1) from earlier studies that is seldom addressed and is discussed, presenting data on a unique association in colon and CRC. Tumor-derived cell lines are quite commonly used for pre-clinical studies involving the role of GPX2 in CRC. Generally, selection for this type of work is limited to identifying cell lines based on high and low GPX2 expression with the standard re-search scheme of overexpression in low expressing lines and suppression in high expressing lines to identify impacted pathways. This overlooks CRC subtypes among cell lines involving a wide range of gene expression profiles and a variety of driver mutation differences along with a large difference in GPX2 expression levels. A trend for low and high GPX2 expressing cell lines to segregate into different CRC subclasses, indicated in this report, suggests that choices based solely on GPX2 levels may provide misleading and conflicting results by disregarding other properties of cell lines and failing to factor in differences in potential protein targets of ROOH. CRC and cell line classification schemes are presented here that were intended to assist workers in performing pre-clinical studies but are largely unnoted in work on GPX2 and CRC. Studies are often initiated on the premise that the transition from normal to CRC is associated with up-regulation of GPX2. This is probably correct. However, the source normal cells for CRC could be almost any colon cell type, some with very high GPX2 levels. These factors are addressed in this study.

In (Venetz et al., 2019), authors rebuilt the essential genome of Caulobacter crescentus through the process of chemical synthesis rewriting and studied the genetic information content at the level of its essential genes. Then, they reduced the native Caulobacter crescentus native Caulobacter NA1000 genome sequence real genome ( 4042929 bp ) to the 785,701-bp reduced synthetic genome. Here we demonstrate the existence of a palindromic-like mirror structure that exists in real genomes and disappears totally in the synthetic genome. This biomathematic meta-organization is based on characteristic proportions of Fibonacci numbers between DNA single strand nucleotides proportions TC / AG on the one hand and TG / AC on the other hand. In both cases, we suggest that this meta-structure enhances the three-dimensional cohesion of the two DNA strands of the genome. We then generalize this study to the different synthetic genomes and synthetic cells published by the Craig Venter Institute on Mycoplasma Mycoides JCVI-syn1.0 (in 2010), JCVI-syn3.0 (in 2016) and JCVI-syn3A (in 2019). Finally, in the discussion section, we extend this study to synthetic genomes of E-Coli and Yeast chromosome XII.

In two previous articles, the extended $(k, t)$--Fibonacci numbers were presented and some of their properties were studied, both in general and particularizing them for the Leonardo numbers. In a second article we study the sum of the extended $(k, t)$--Fibonacci numbers as well as the sums of these odd and even numbers.\\ In this article we study the sum of the squares of these numbers with their properties as well as the generating function, the recurrence relation and the Binet formula.\\ Finally we particularize these results for the generalized $t$--Leonardo numbers.

In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

This article develops a multi-perspective view on motivations and methods for tobamovirus purification through the ages, and presents a novel efficient, easy-to-use approach that can be well-adapted to different species of native and functionalized virions. We survey the various driving forces prompting researchers to enrich tobamoviruses: from the search for the causative agents of mosaic diseases in plants to their increasing recognition as versatile nanocarriers in biomedical and engineering applications. Best practice and also rarely applied options for the serial processing steps required for successful isolation of tobamoviruses are then reviewed. Adaptations for distinct particle species, pitfalls and 'forgotten' or underrepresented technologies are considered as well. The article is topped off with our own development of a method for virion preparation, rooted in historical protocols. It combines selective re-solubilization of polyethylene glycol (PEG) virion raw precipitates with density step gradient centrifugation in biocompatible iodixanol formulations, yielding ready-to-use particle suspensions. This newly established protocol and some considerations for perhaps worthwile further developments could serve as putative stepping stones towards preparation procedures appropriate for routine practical uses of the multivalent soft-matter nanorods.

2019-n-CoV is the seventh coronavirus known to infect humans and cause serious illness, and due to its lethality there was a worldwide mobilization for the development of new drugs and new vaccines for Covid-19. Therefore, the present work aims to carry out a virtual screening of terpenes with potential anti SARS-CoV-2 activity. To perform the ligand-based virtual, a model was constructed regarding the compounds which already showed inhibitory activity of the SARS-CoV-2. The test series corresponded to terpenes isolated in the Fabaceae Family. The compounds that were most likely to activity were subjected to Molecular Docking and the best poses obtained were subjected to Molecular Dynamics (MD) simulations carried. The molecules under study were submitted to in vitro evaluation to assess inhibitory activity of compounds against SARS-CoV-2 in a phenotypic screening model of the virus. The compounds selected by in silico screening corresponded to triterpenoids from the lupane series. In the in vitro test, both demonstrated activity against the SARS-CoV-2 virus. The virtual screening performed managed to identify the compounds with the highest probability of activity, as well as the most stable compounds, and the method used was validated by the in vitro study carried out.

Bees (Apoidea), the largest and most crucial radiation of pollinators, play a vital role in ecosystem balance. Transposons are widely distributed in nature and are important drivers of species diversity. However, transposons are rarely reported in important pollinators such as bees. Here, we surveyed 37 genomes in Apoidea, annotated the pogo and Tc1/mariner transposons in the genome of each species and performed a phylogenetic analysis to determine their overall distribution. The pogo and Tc1/mariner families showed high diversity and low abundance in the 37 species, and their proportion was significantly higher in solitary bees than in social bees. DD34D/mariner was found to be distributed in almost all species and was found in Apis mellifera, Apis mellifera carnica, Apis mellifera caucasica and Apis mellifera mellifera and Euglossa dilemma may still be active. Using horizontal transfer analysis, we found that DD30D/Tigger, DD33D/Tigger and DD34D/mariner may have experienced horizontal transfer events. The current study displayed the evolution profiles (including diversity, activity, and abundance) of the pogo and Tc1/mariner transposons across 37 species of Apoidea. Our data revealed their contributions to the genomic variations across these species and facilitated in understanding of the genome evolution of this lineage.

We evaluate various sums involving the powers of Fibonacci and Lucas numbers.

Reconstructing the Tree of Life remains a central goal in biology. Early methods, relying on small numbers of morphological or genetic characters, often yielded conflicting evolutionary histories, undermining confidence in the results. Investigations based on phylogenomics, which use hundreds to thousands of loci for phylogenetic inquiry, have provided a clearer picture of life's history, but certain branches remain problematic. To resolve difficult nodes on the Tree of Life, two recent studies tested the utility of synteny, the conserved collinearity of orthologous genetic loci in two or more organisms, for phylogenetics. Synteny exhibits compelling phylogenomic potential while also raising new challenges. We identify and discuss specific opportunities and challenges that bear on the value of synteny data and other rare genomic changes for phylogenomic studies. Synteny-based analyses of highly contiguous genome assemblies mark a new chapter in the phylogenomic era and the quest to reconstruct the Tree of Life.

Centromeres, the chromosomal loci where spindle fibers attach during cell division to segregate chromosomes, are typically found within satellite arrays in plants and animals. Satellite arrays have been difficult to analyze because they comprise megabases of tandem head-to-tail highly repeated DNA sequences. Much evidence suggests that centromeres are epigenetically defined by the location of nucleosomes containing the centromere-specific histone H3 variant cenH3, independently of the DNA sequences where they are located; however, the reason that cenH3 nucleosomes are generally found on rapidly evolving satellite arrays has remained unclear. Recently, long read sequencing technology has clarified the structures of satellite arrays and sparked rethinking of how they evolve, while new experiments and analyses have helped bring both understanding and further speculation about the role these highly repeated sequences play in centromere identification.

The early elongation events in transcription or translational control in the N-terminal of genes are assuming critical roles in their heterologous expression. The secretory expression of the alkaline pectin lyase APL in B. subtilis were studied to explore the effects of the N-terminal 5-7 amino acids sequences of different signal peptides on gene transcription and protein secretion in this study. The first 5 amino acid sequences of the N-terminal of the signal peptide LipA were identified to play an important role in promoting the expression of APL for the first time. Meanwhile, it also revealed that the signal peptide LipA could lead to higher secretory expression than other signal peptides not because of its sequence structure associated with secretion is stronger but because the N-terminal sequences showed greater advantages in gene transcription. At this basis, the recombinant strain structed in this work showed a new record for the highest extracellular yields (12 295 U/ml) of APL in B. subtilis which was 1.9 times higher than that expressed in the recombinant Escherichia coli strain we had reported before. The novel theories revealed in this study would assuming significance roles for improving expression of foreign proteins in or out of the cells.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

We evaluate some binomial cubic Fibonacci sums.

We evaluate various binomial sums involving the powers of Fibonacci and Lucas numbers.

Oral squamous cell carcinoma (OSCC) is a highly prevalent and aggressive malignancy, with mortality rates that reach 60%, mainly due to an excessive diagnostic delay. MiRNAs, a class of crucial epigenetic gene-expression regulators, have emerged as potential diagnostic biomarkers, with >200 molecules reported to be dysregulated in OSCC. We had previously established an in silico methodology for the identification of the most disease-specific molecules by bridging genetics and epigenetics. Here, we identified the stage-specific miRNAs that govern the asymptomatic early stages of oral tumorigenesis by exploiting the reverse interplay between miRNA-levels and their target-genes’ expression. Incorporating gene expression data from our group’s experimental hamster model of sequential oral oncogenesis, we bioinformatically detected the miRNAs that simultaneously target/regulate >75% of the genes that are characteristically upregulated or downregulated in the consecutive stages of hyperplasia, dysplasia and early-invasion OSCC, while exhibiting the opposite expressional dysregulation in OSCC-derived tissue and/or saliva specimens. We found that all stages share the downregulation of miR-34a-5p, miR124-3p, and miR-125b-5p, while miR-1-3p is underexpressed in dysplasia and early-invasion. Malignant early-invasion stage is distinguished by the downregulation of miR-147a and the overexpression of miR-155-5p, miR-423-3p and miR-34a-5p. The identification of stage-specific miRNA molecules may facilitate their utilization as biomarkers for presymptomatic OSCC diagnosis.

The vast array of omics data in microbiology presents significant opportunities for studying bacterial pathogenesis and creating computational tools for predicting pathogenic potential. However, the field lacks a comprehensive, curated resource that catalogs bacterial strains and their ability to cause human infections. Current methods for identifying pathogenicity determinants often introduce biases and miss critical aspects of bacterial pathogenesis.In response to this gap, we introduce BacSPaD (Bacterial Strains’ Pathogenicity Database), a thoroughly curated database focusing on pathogenicity annotations for a wide range of high-quality, complete bacterial genomes. Our rule-based annotation workflow combines metadata from trusted sources with automated keyword matching, extensive manual curation, and detailed literature review. Our analysis classified 5,502 genomes as pathogenic to humans (HP) and 490 as non-pathogenic to humans (NHP), encompassing 532 species, 193 genera, and 96 families. Statistical analysis demonstrated a significant but moderate correlation between virulence factors and HP classification, highlighting the complexity of bacterial pathogenicity and the need for ongoing research. This resource is poised to enhance our understanding of bacterial pathogenicity mechanisms and aid in the development of predictive models. To improve accessibility and provide key visualization statistics, we developed a user-friendly web interface, accessible at https://bacspad.altrabio.com.

Alignment of picornavirus proteinase/polymerase sequences reveals this family evolved into five ‘supergroups’. Interestingly, the nature of the 2A region of the picornavirus polyprotein is highly correlated with this phylogeny. Viruses within supergroup 4, the Paavivirinae, have complex 2A regions with many viruses encoding multiple 2A^NPGP sequences. In vitro transcription/translation analyses of a synthetic polyprotein comprising green fluorescent protein (GFP) linked to b-glucuronidase (GUS) via individual 2A^NPGPs showed two main phenotypes: highly active 2A^NPGP sequences - similar to Foot-and-Mouth Disease Virus 2A^NPGP and, surprisingly, a novel phenotype of some 2A^NPGP sequences which apparently terminate translation at the C-terminus of 2A^NPGP - without detectable re-initiation of downstream sequences (GUS). Probing databases with the short sequences between 2A^NPGPs did not reveal any potential ‘accessory’ functions. The novel, highly active, 2A-like sequences we identified substantially expands the toolbox for biomedical / biotechnological co-expression applications.

The article explores the concept of 'synthetic man' (SM) in the context of 'synthetic biology' (SB), analysing the potential, challenges, and ethical implications of these achievements. Through dialogue with ChatGPT 4, an in-depth understanding of the evolution, contributions of SM, ChatGPT's contribution, and concerns associated with SM is sought, providing insight into how this technology could affect our society. Our study uses a structured dialogue framework with ChatGPT that addresses essential SM questions regarding SM history, contributions, challenges, and concerns. ChatGPT responses are analysed to extract relevant information and identify trends and insights. The ChatGPT dialogue reveals that MS is still a theoretical and speculative concept with significant advances in gene therapy and genetic engineering. The potential contributions of SM in addressing global challenges such as health, environment and education are identified. Ethical and social concerns such as health risks and psychological impact are also highlighted. Differences in ChatGPT responses were observed between different sessions or even within the same session, which highlighted the limitations in the replicability of the research and sometimes the need for clarification of the questions. The article is distinguished by its unique approach of using an advanced language model to explore a complex and speculative topic. The LLM Dialogue Framework on Technology (LLM-DFonTech) framework proposal for structured dialogue with ChatGPT on various technological topics related to the original contribution provides an adaptable tool for interdisciplinary research in emerging technologies. This methodology opens up new possibilities for analyzing and developing trends in technology and society.

Horizontal transfer of transposons (HTT) is an important source of genomic evolution in eukaryotes. The HTT dynamics is well characterized in eukaryotes including insects however, but there is a huge gap of knowledge about HTT regarding many eukaryotes’ species. In this study we analyzed the events of the HTT between Rhus gall aphids (Hemiptera) and other insects. We analyzed the Mariner-like transposable elements (MLEs) belongs to Rhus gall aphids for the possible HT events. The MLEs have patchy distribution and have high similarity over the entire length of element with insects MLEs from different orders. We selected representative sequences from the Rhus gall MLEs and identified five events of HT between MLEs of Rhus gall aphids and other insects from five different orders. We also found multiple HTT events among the MLEs of insects from the five orders which demonstrate that these Mariner elements have been involved in recurrent HT between these six order of insects. Our current study closed the knowledge gap of HTT and reported the events between Rhus gall aphids and other insects for the first time. We believe that this study about HTT events will help to understand the evolution and spread of transposable elements in the genomes of Rhus gall aphids.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

Complex interactions between gene variants and environmental risk factors underlie the pathophysiological pathways in major psychiatric disorders. Autism Spectrum Disorder is a psychiatric condition in which susceptible alleles along with epigenetic memories contribute to the mutational landscape of the ailing brain. The present work reviews recent evolutionary, molecular, and epigenetic mechanisms potentially linked to the etiology of autism. First, we present a clinical vignette to describe clusters of maladaptive behaviors frequently diagnosed in autistic patients. Next, we microdissect brain regions pertinent to the nosology of autism as well as cell networks from the bilateral body plan. Lastly, we catalog a number of pathogenic environments associated with disease risk factors. This set of perspectives provides emerging insights into the dynamic interplay between epigenetic and environmental variation in the development of Autism Spectrum Disorders.

Fetal Alcohol Spectrum Disorders (FASD) represent a continuum of lifelong impairments resulting from prenatal exposure to alcohol, with significant global impact. The “spectrum” of disorders includes a continuum of physical, cognitive, behavioral, and developmental impairments, which can have profound and lasting effects on individuals throughout their lives impacting their health, social interactions, psychological well-being and every aspect of their lives. This narrative paper explores the intricate relationship between oxidative stress and epigenetics in FASD pathogenesis and its therapeutic implications. Oxidative stress, induced by alcohol metabolism, disrupts cellular components, particularly in the vulnerable fetal brain, leading to aberrant development. Furthermore, oxidative stress is implicated in epigenetic changes, including alterations in DNA methylation, histone modifications, and microRNA expression, which influence gene regulation in FASD patients. Moreover, mitochondrial dysfunction and neuroinflammation contribute to epigenetic changes associated with FASD. Understanding these mechanisms holds promise for targeted therapeutic interventions. This includes antioxidant supplementation and lifestyle modifications to mitigate FASD-related impairments. While preclinical studies show promise, further clinical trials are needed to validate these interventions' efficacy in improving clinical outcomes for individuals affected by FASD. This comprehensive understanding of the role of oxidative stress on epigenetics in FASD underscores the importance of multidisciplinary approaches for diagnosis, management, and prevention strategies. Continued research in this field is crucial for advancing our knowledge and developing effective interventions to address this significant public health concern.

Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

Histones display a wide variety of post-translational modifications, including acetylation, methylation, and phosphorylation. These epigenetic modifications can influence chromatin structure and function without altering the DNA sequence. Histones can also undergo post-translational O-GlcNAcylation, a rather understudied modification that plays critical roles in almost all biological processes and is added and removed by O-linked N-acetylglucosamine transferase and O-GlcNAcase, respectively. This review provides a current overview of our knowledge of how O-GlcNAcylation impacts the histone code both directly and by regulating other chromatin modifying enzymes. This highlights the pivotal emerging role of O-GlcNAcylation as an essential epigenetic marker.

Thioethers are critical in the fields of pharmaceuticals and organic synthesis, but most of the methods for synthesizing alkyl thioethers employ foul-smelling thiols as starting materials or generate them as by-products. Additionally, most thiols are air-sensitive and are easily oxidized to produce disulfides under atmospheric conditions; thus, a novel method for synthesizing thioethers is necessary. This paper reports a simple, effective, green method for synthesizing dialkyl or alkyl aryl thioether derivatives using odorless, stable, low-cost ROCS2K as a thiol surrogate. This transformation offers a broad substrate scope and good functional group tolerance with excellent selectivity. The reaction likely proceeds via xanthate intermediates, which can be readily generated via the nucleophilic substitution of alkyl halides or aryl halides with ROCS2K under transition-metal-free and base-free conditions.

In this study, we demonstrate the direct preparation of dihalo-γ-lactams featuring two distinct halogens from dichloroamides using a novel Atom Exchange Radical Cyclization (AERC) procedure. This method integrates the established Atom Transfer Radical Cyclization with halogen exchange in solution. The technique operates under mild conditions and requires little amounts of metallic copper, serving as both a supplemental activator and reducing agent.

Here, we describe the bicomplex (p,q)- Fibonacci numbers and the bicomplex (p,q)- Fibonacci quaternions that are based on these numbers and give some of their equations, including the Binet formula, generating function, Catalan, Cassini, d’Ocagne’s identities, and some summation formulas for both of them. Finally, we create a matrix for bicomplex (p,q)- Fibonacci quaternions, and we obtain a determinant of a special matrix that gives the terms of that quaternion.

Epidemiological data highlight prostate cancer as a significant global health issue, with high incidence and substantial impact on patients' quality of life. The prevalence of this disease is associated with various factors, including age, heredity, and race. Recent research in prostate cancer genetics has identified several genetic variants that may be associated with an increased risk of developing the disease. However, despite the significance of these findings, genetic markers for prostate cancer are not currently utilized in clinical practice as reliable indicators of the disease. In addition to genetics, epigenetic alterations also play a crucial role in prostate cancer development. Aberrant DNA methylation, changes in chromatin structure, and microRNA (miRNA) expression are major epigenetic events that influence oncogenesis. Existing markers for prostate cancer, such as prostate-specific antigen (PSA), have limitations in terms of sensitivity and specificity. The cost of testing, follow-up procedures, and treatment for false-positive results and overdiagnosis contributes to the overall healthcare expenditure. Improving the effectiveness of prostate cancer diagnosis and prognosis requires either narrowing the risk group by identifying new genetic factors or enhancing the sensitivity and specificity of existing markers. Immunological biomarkers (both circulating and intra-tumoral), including markers of immune response and immune dysfunction, represent a potentially useful area of research for enhancing the diagnosis and prognosis of prostate cancer. Our review emphasizes the need for developing novel immunological biomarkers to improve the diagnosis, prognosis, and management of prostate cancer. We highlight the most recent achievements in the identification of biomarkers provided by circulating monocytes and tumor-associated macrophages (TAMs). We highlight that monocytes-derived and TAMs-derived biomarkers can enable to establish the missing links between genetic predisposition, hormonal metabolism and immune responses in prostate cancer.

Precision metagenomic approaches using Oxford Nanopore Technology (ONT) sequencing has been shown to allow recovery of complete genomes of Escherichia coli O157:H7 from overnight enrichments of agricultural waters. This study tests the applicability of a similar approach for Cronobacter genome recovery from powdered infant formula (PIF) overnight enrichments, where Cronobacter typically dominates the overall microbiome (>90%). In this study, we aimed to test whether using ONT sequencing of overnight PIF enrichments could recover a completely closed Cronobacter genome for further genomic characterization. Ten PIF samples, each inoculated with different Cronobacter strains, covering Cronobacter sakazakii, C. muytjensii, C. dublinensis, C. turicensis, and C. universalis, were processed according to the Bacteriological Analytical Manual (BAM) protocol. qPCR was used for initial screening (detection and quantification) of the overnight enrichments and confirmed that the spiked PIF samples after the overnight enrichment have high levels of Cronobacter (107 to 109 CFU/mL). DNA from overnight PIF enrichments was extracted from the enrichment broth and sequenced using ONT. Results showed that ONT sequencing could accurately identify, characterize, and close the genomes of Cronobacter strains from overnight PIF enrichments in 3 days, much faster than the nearly two weeks required by the current BAM method. Complete genome recovery and species differentiation were achieved. This suggests that combining qPCR with ONT sequencing provides a rapid, cost-effective alternative for detecting and characterizing Cronobacter in PIF, enabling timely corrective actions during outbreaks.

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

Plant breeding conventionally depends on genetic variability available in a species to improve a particular trait in the crop. However, epigenetic diversity may provide an additional tier of variation. The recent advent of epigenome technologies has elucidated the role of epigenetic variation in shaping phenotype. Further, the development of epigenetic recombinant inbred lines (epi-RILs) in the model species such as Arabidopsis has enabled accurate genetic analysis of epigenetic variation. Subsequently, mapping of epigenetic quantitative trait loci (epiQTL) allowed association between epialleles and phenotypic traits. Thus, quantitative epigenetics provides ample opportunities to dissect the role of epigenetic variation in trait regulation, which can be eventually utilized in crop improvement programs. Moreover, locus-specific manipulation of DNA methylation by epigenome-editing tools such as clustered regularly interspaced short palindromic repeats/CRISPR-associated protein 9 (CRISPR/Cas9) can facilitate epigenetic based molecular breeding of important crop plants.

Background: The resurgence of syphilis, primarily in MSM populations, has necessitated novel prophylactic strategies, such as the use of doxycycline post-exposure prophylaxis (doxy-PEP). However, the potential for increased doxycycline use to select for tetracycline resistance represents significant challenges in managing this sexually transmitted infection. This study aims to identify chromosomal mutations associated with tetracycline resistance in Spirochaetales to inform treatment strategies and surveillance measures.Methods: Whole genome sequences (WGS) from the Spirochaetales order, including 4,355 genomes, were analyzed for the presence of mutations in 16S rRNA and non-synonymous mutations in the rpsC and rpsJ genes. The study utilized WGS from GenBank® and sequence data from the PubMLST Treponema pallidum isolate collection. Genetic resistance to tetracycline was detected using a combination of BLASTN searches and gene-gene analysis. Results: A transition mutation TGA to TGG at positions 965-967 in the 16S rRNA gene was detected in 5.6% of Treponema spp. and 3.97% of Spirochaeta spp. genomes. The rpsJ gene exhibited a V57G amino acid substitution across a significant subset of Treponema spp. Notably, the V57K mutation was common in Spirochaeta spp. The rpsC gene had the H178Q mutation and was found to be present in the Spirochaetales bacterium.Conclusion: The identification of mutations associated with tetracycline resistance in Spirochaetales provides a foundation for the development of rapid molecular diagnostics and guides the clinical selection of antibiotics for syphilis treatment. This study underscores the complexity of antibiotic resistance mechanisms and the critical importance of surveillance in the era of antibiotic prophylaxis for STI management.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

KLHL genes and the related KBTBD genes encode components of the Cullin-E3 ubiquitin ligase complex and typically target tissue-specific proteins for degradation, thereby affecting differentiation, homeostasis, metabolism, cell signaling, and the oxidative stress response. Despite their importance in normal cell function and in disease (KLHL40, KLHL41, KBTBD13, KEAP1, and ENC1), previous studies that examined epigenetic factors affecting transcription were predominantly limited to promoter DNA methylation. Using diverse tissue and cell culture whole-genome profiles, we examined 17 KLHL or KBTBD genes preferentially expressed in skeletal muscle or brain to identify tissue-specific enhancer and promoter chromatin, open chromatin (DNaseI hypersensitivity), and DNA hypomethylation. Sixteen of the 17 genes displayed muscle- or brain-specific enhancer chromatin in their gene bodies, and most exhibited specific intergenic enhancer chromatin as well. Seven genes were embedded in a super-enhancer. The enhancer chromatin regions typically displayed foci of DNA hypomethylation at peaks of open chromatin. In addition, we found evidence that gene neighbors (HHATL and FBXO32) of KLHL40 and KLHL38 harbor enhancer chromatin that likely upregulates the adjacent KLHL gene. Many KLHL/KBTBD genes had tissue-specific promoter chromatin at their 5’ ends, but surprisingly, two (KBTBD11 and KLHL31) had constitutively unmethylated promoter chromatin in their 3’ exons that overlaps a retrotransposed KLHL gene. Our findings demonstrate the importance of expanding epigenetic analyses beyond the 5’ ends of genes in studies of normal and abnormal gene regulation.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

We describe the genomes of two Echovirus isolates from Nigeria as reference enterovirus species B genomes for the region. These Echovirus 7 and 19 genomes have 7,411nt and 7,426nt, and were recovered from sewage contaminated water (in 2010) and an acute flaccid paralysis case (in 2014), respectively.

This article presents description of social structures such as, for example, states, in the context of their consideration as systems. Moreover, it seeks to develop K. Marx’s model in terms of systematic approach, as well as to justify the application of the Fibonacci sequence to systems in general and, in particular, to social systems. The description covers a wide range of issues, ranging from the assertion of the basic principle of living systems as patterns in resources flows to description of functions of various aspects of states and their economics in terms of objective needs of such structures. In addition, this article justifies synergetic effect based on proposed model, and the way this effect is applied to state systems. Moreover, it includes the description of main changes of socio-economic formations throughout the history as a natural development of social systems, including possible modern stages. The fundamental tool of this description is description of essence of the mechanism of property rights and its formation options. The differences of two extreme directions of such development are also described on the basis of the objective factor of resource provision. Special attention is given to the concept of surplus value as a feature of social production systems.

Autism spectrum disorder (ASD) is a neurodevelopmental disease characterized by persistent deficits in social interaction and communication, repetitive movements, abnormal focusing on objects, or activity that can significantly affect the quality of life of the afflicted. Brain neuronal and glial cells have been implicated. It has a genetic component but can also be triggered by environmental factors or drugs. For example, prenatal exposure to valproic acid (VPA) or acetaminophen (APAP) or ingestion of propionic acid (PPA) can increase the risk of ASD. Recently, epigenetic influences on ASD have been brought to the forefront of investigations on the etiology, prevention, and treatment of this disorder. Epigenetics refers to DNA modifications that alter gene expression without making any changes to the DNA sequence. Although an increasing number of pharmaceuticals and environmental chemicals are being implicated in the etiology of ASD, here we specifically focus on the molecular influence of the above-mentioned drugs on epigenetic alterations in neuronal and glial cells and their potential connection to ASD. It is concluded that a better understanding of these phenomena can lead to more effective interventions in ASD.

Epigenetic reprogramming represents a series of essential events during many cellular processes including oncogenesis. Genome of Kaposi’s sarcoma-associated herpesvirus (KSHV), an oncogenic herpesvirus is predetermined for a well-orchestrated epigenetic reprogramming once it enters into a host cell. The initial epigenetic reprogramming of KSHV genome allow restricted expression of encoded genes and helps to hide from host immune recognition. The infection with KSHV is associated with Kaposi's Sarcoma, Multicentric Castleman's disease, KSHV inflammatory cytokine syndrome and primary effusion lymphoma. The major epigenetic modifications associated with KSHV can be labelled under three broad categories: DNA methylation, modifications of Histone, and the role of noncoding RNAs. These epigenetic modifications significantly contribute towards the latent-lytic switch of the KSHV lifecycle. This review gives a brief account of the major epigenetic modifications affiliated with the KSHV genome in infected cells and their impact on pathogenesis.

Epimutations are the cause of a considerable number of genetically inherited conditions in humans. All result from the mis-expression of genes due to epigenetic changes that are triggered by an underlying heritable mutation. The correction of these epigenetic defects in the context of epigenetically regulated diseases constitutes a good paradigm to probe the fundamental mechanisms underlying the development of these diseases, and the molecular basis for the establishment, maintenance and regulation of epigenetic modifications in general. Here, we review current applications of key editing tools to address the epigenetic aspects of these diseases by focusing on epimutations caused by, or relate to repetitive elements, primarily unstable noncoding repeat expansions. For each approach we summarize the efforts conducted to date, highlight their contribution to a better understanding of the molecular basis of epigenetic mechanisms, describe the limitations of each approach and suggest perspectives for further exploration in this field.

Epigenetics, the study of heritable changes in gene expression that do not involve alterations to the DNA sequence, is revolutionizing our understanding of psychiatric disorders. This article provides a comprehensive overview of the role of epigenetics in psychiatry, discussing its implications for genomics, evolution, inheritance patterns, and the development of biomarkers. Epigenetic mechanisms, including DNA methylation, histone modifications, and non-coding RNAs, are explored in the context of psychiatric conditions such as depression, schizophrenia, and post-traumatic stress disorder (PTSD). The discussion highlights how epigenetic modifications can influence brain dynamics, as measured by electroencephalography (EEG), and how artificial intelligence (AI) can accelerate the development of treatment options. The potential for epigenetic biomarkers to improve diagnosis, prognosis, and treatment is emphasized, along with the role of behavioral interventions in inducing beneficial epigenetic modifications. Future directions in epigenetic research, including the development of epigenetic therapies and the elucidation of molecular mechanisms underlying epigenetic inheritance, are also discussed. This article underscores the transformative potential of epigenetics in advancing our understanding of mental health and disease, paving the way for novel therapeutic interventions.

Very disparate types of cell populations exhibit similar transcription specificity for certain genes. We identified 20 genes that were expressed preferentially in myoblasts and cerebellum (Myob/Cbl genes) and examined their cell/tissue-specific epigenetics using a combined approach of comparing DNA methylation, chromatin accessibility, and RNA expression in many different cell populations. Some Myob/Cbl genes shared DNA hypo- or hypermethylated regions in myoblasts and cerebellum. Particularly striking was ZNF556, whose promoter is hypomethylated in expressing cells but highly methylated in the many cell populations that do not express the gene. In reporter gene assays, we demonstrated that its promoter’s activity is methylation-sensitive. The atypical epigenetics of ZNF556 may have originated from its promoter’s hypomethylation and selective activation in sperm progenitors and oocytes. Five of the Myob/Cbl genes (KCNJ12, ST8SIA5, ZIC1, VAX2, and EN2) have much higher RNA levels in cerebellum than in myoblasts and displayed myoblast-specific hypermethylation upstream and/or downstream of their promoters that may downmodulate expression. Differential DNA methylation was associated with alternative promoter usage for Myob/Cbl genes MCF2L, DOK7, CNPY1, and ANK1. Myob/Cbl genes PAX3, LBX1, ZNF556, ZIC1, EN2, and VAX2 encode sequence-specific transcription factors, which likely help drive the myoblast and cerebellum specificity of other Myob/Cbl genes. Our study extends our understanding of epigenetic/transcription associations related to differentiation and may help elucidate relationships between epigenetic signatures and muscular dystrophies or cerebellar-linked neuropathologies.

Globally, humans are struggling with the double threat of communicable and non-communicable diseases, which are presenting new challenges to public health. Public health problems are generally studied and addressed at primary, secondary and tertiary levels. Most effective results are seen with primary interventions. Public health is becoming more aware of the importance of environment-gene interactions in the ontology of health and disease using epigenetics. Epigenetics is the study of altered gene expression without change in base pairs. Be it physical, social, behavioral, or economic factors; they all influence quality of life and health of individuals and populations. That environments are changing the human health phenotype and these changed phenotypes are heritable is of concern for the future of the human race. Knowing the causes of non-communicable human diseases using epigenetics will contribute to the development of new policies to encourage prevention using primary public health initiatives. Research and application of epigenetics shows great promise for improving population health. Continued advances in epigenetics will enhance how we understand and address the way environments are affecting the human health phenotype. For some time, health systems have been and continue to be tertiary in nature. Epigenetic changes can provide information necessary to better understand how social determinants of health can be used to build societies focused on equitable health for all people, rather than continuing to focus on treatment of diseases in the tertiary phase that leads to health disparities. Understanding mechanisms of social determinants of disease, will allow society to evolve in a health-oriented rather than a disease-oriented world. For this reason, we must enhance and apply epigenetics (physical, social, behavioral, economic) research to policy development. We will discuss how bringing social determinants together with biology can be used as new tools for public health policy.

Chikungunya virus (CHIKV) is a mosquito borne RNA virus that poses an emerging threat to humans. As other RNA viruses, CHIKV encodes an error-prone RNA polymerase which, in addition to full-length genomes, gives rise to truncated, non-functional genomes coined defective viral genomes (DVGs). DVGs have been intensively studied in the context of therapy, as they can inhibit viral replication and dissemination in their hosts. In this work, we interrogate the influence of viral RNA secondary structures on the production of CHIKV DVGs. We experimentally map RNA secondary structures of CHIKV genome using selective 2′-hydroxyl acylation analyzed by primer extension and mutational profiling (SHAPE-MaP), which couples chemical labelling with next-generation sequencing. We correlate the inferred secondary structure with preferred deletion sites of CHIKV DVGs. We document an increased probability of DVG generation with truncations at unpaired nucleotides within the secondary structure. We then generated a CHIKV mutant bearing synonymous changes at the nucleotide level to disrupt existing RNA secondary structure (CHIKV-D2S). We show that CHIKV-D2S presents altered DVG generation compared to wild-type virus, correlating with its change in RNA secondary structure obtained by SHAPE-MaP. Our work thus demonstrates that RNA secondary structure impacts CHIKV DVG production during replication.

Repetitive elements are a major component of DNA sequences due to their ability to propagate through the genome. Characterization of Metazoan repetitive profiles is picking up, however, current pipelines are failing to identify a significant proportion of divergent repeats in non-model organisms. The order Decapoda, for which repeat content analyses are largely lacking, is characterized by extremely variable genome sizes that suggest an important presence of repetitive elements. Here we developed a new standardized pipeline to annotate repetitive elements in non-model organisms, which we applied on 20 Decapoda and 6 other crustacean genomes. With our new tool we identify 10% more repetitive elements than standard pipelines. Repetitive elements were more abundant in Decapoda species than in other crustaceans, with an incredibly large number of highly repeated satDNA families. Moreover, we demonstrated a high correlation between assembly size and transposable elements and a different repeat dynamics between Dendrobranchiata and Reptantia. The patterns of repetitive elements largely reflect the phylogenetic relationships of Decapoda and the distinct evolutionary trajectories within Crustacea. In summary, our results highlight the impact of repetitive elements on genome evolution in Decapoda and the value of our novel annotation pipeline, which will provide a baseline for future comparative analyses.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

Modification of electrode surface with a selective layer gives the possibility to detect target ana-lytes of forensic interest. 3-(4-trifluoromethyl)-phenyl)-thiophene (ThPhCF3) was deposited on a graphite (G) electrode by electrochemical oxidation and characterized as a receptor for the recognition of synthetic stimulants (2-aminoindane, buphedrone, naphyrone). First, the structural characterization of the polymeric layer were obtained from Raman spectroscopy. Second, the electrochemical profiles of selected synthetic stimulants and their affinity to ThPhCF3/G-modified electrodes were studied using square wave voltammetry and electrochemical impedance spec-troscopy. The values of the adsorption constant show the importance of – PhCF3 groups in the interaction with synthetic stimulants, namely recognition by the formation of hydrogen bonds (Kads (buphedrone) < Kads (2-AI)) and interaction with aromatic H atoms (Kads (buphedrone) < Kads (naphyrone)). It was demonstrated that the polymeric layer derived from thiophene with – PhCF3 group is capable to increase the intensity of the electrochemical signal.

Sporadic Alzheimer’s disease (AD) derives from an interplay among environmental factors and genetic variants, while epigenetic modifications have been expected to affect the onset and progression of its complex etiopathology. Heterozygous carriers of the apolipoprotein E gene (APOE)4 allele have a 4-fold increased risk of developing AD, while APOE 4/4-carriers have a 12-fold increased risk in comparison with the APOE 3-carriers. The main longevity factor is the homozygous APOE ε3/ε3 genotype. In the present narrative review article, we summarized and described the role of APOE epigenetics in aging and AD pathophysiology. It is not fully understood how APOE variants may increase or decrease AD risk, but this gene is known to affect amyloid- and tau-mediated neurodegeneration directly or indirectly, also by affecting lipid metabolism and inflammation. For sporadic AD, epigenetic regulatory mechanisms may control and influence APOE expression in response to external insults. Diet, a major environmental factor, has been significant associated with physical exercise, cognitive function, and the methylation level of several cytosine-phosphate-guanine (CpG) dinucleotides sites of APOE.

Climate change has had a significant impact on many ecosystems worldwide, prompting native population species to adapt to the current weather patterns eventually. Pre-existing genetic variation in populations explains part of this adaptation. Still, recent studies have shown that new stable phenotypes can be generated through epigenetic modifications in just a few generations, thereby contributing to the stability and survival of plants in their natural habitat as they eventually adjust to the surrounding impacts. The state of chromatin inside plant cells varies, allowing cells to fine-tune their transcriptional profiles to better adapt to stimuli from the external environment. Within a cell, chromatin state changes such as post-transcriptional histone modifications and variations, DNA methylation, and non-coding RNA activity are all examples of chromatin state alterations that may epigenetically dictate certain transcriptional outputs. Recent advances in the field of ‘Omics’ in major crops has made it easier to identify epigenetic changes and their impact on plant responses to environmental stresses. These epigenetic mechanisms thus play an important role in improving crop adaptation and resilience to changing environments. This variation that has emerged can thus be exploited in crop breeding, ultimately leading to the generation of stable climate-resilient genotypes.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

In view of the Practical Byzantine Fault Tolerance (PBFT) consensus algorithm all nodes participate in the consensus, the three-stage process has problems such as large communication overhead, random selection of master nodes and lack of reward and punishment mechanism. A Speculative Practical Byzantine Fault Tolerance (SP-PBFT) is proposed. Firstly, the consensus protocol was optimized, and a timeout mechanism was proposed to divide the consensus process into optimistic mode and pessimistic mode, which reduced the communication overhead under the premise of resisting Byzantine node attacks .Secondly, a node evaluation mechanism was proposed to calculate the node reputation value according to the node's historical behavior and give the corresponding reward or punishment, which reduced the possibility of malicious nodes participating in the consensus process. Finally, the Fibonacci grouping mechanism was used to reduce the number of nodes participating in the consensus process, fundamentally improving the consensus efficiency, avoiding the problem of centralization of the consensus process caused by the cumulative reputation value of nodes, and improving the enthusiasm of consensus nodes. Simulation experiments using Docker containers to simulate multiple nodes show that the SP-PBFT consensus algorithm proposed in this paper has better performance than PBFT consensus algorithm and other improved algorithms in terms of consensus delay, throughput, fault tolerance and communication complexity.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

The severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) viral genome is an RNA virus consisting of approximately 30,000 bases. As part of testing efforts, whole genome sequencing of human isolates has resulted in over 1,600 complete genomes publicly available from GenBank. We have performed a comparative phylogenetic analysis of the sequences, in order to detect common mutations within the population. Analysis of variants occurring within the assembled genomes yields 417 variants occurring in at least 1% of the completed genomes, including 229 within the 5’ untranslated region (UTR), 152 within the 3’UTR, 2 within intergenic regions and 34 within coding sequences.

Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown.

ABSTRACT. In this paper, we suggest a biomathematical numerical method for analysing mRNA nucleotides sequences based on UA/CG Fibonacci numbers proportions. This method is used to evaluate then compare the spike genes related to the main SARS-CoV2 VARIANTS currently circulating within the world population. The 10 main results proposed to be reproduced by peers are: 1/ SARS-CoV2 genome and spike evolution in one year 2020-2021. 2/ SARS-CoV2 Origins. 3/ Comparing 11 reference variants spikes. 4/ analysing 32 CAL.20C California variant patients spikes. 5/ Toward a meta mRNA Fibonacci gene end message code. 6/ Analysing S501 UK, S484 South Africa and « 2 mutations » INDIA variants. 7/ Suggesting a possible variants spike mRNA palindrome symmetry metastructure improving mRNA stability then infectiousness. 8/ Analysing Fibonacci Metastructures in the mRNA coding for the vaccines PFIZER and MODERNA. 9/ Does the CG-rich modification of the synonymous codons of the spikes of the 2 mRNA vaccines affect the expression and quantity of SARS-CoV2 antibodies? 10/ The exceptional case of the Brazilian variant P.1. Particularly, we suggest the following conjecture at mRNA folding level : CONJECTURE of SARS-CoV2 VARIANTS: The growth of long Fibonacci structures in the shape of "podiums" for almost all of the variants studied (UK, California, South Africa, India, etc.) suggests the probable folding of the Spike mRNA in the form of a "hairpin", which can strengthen the cohesion and the lifespan of this mRNA. Finally, we show that these kinds of Fibonacci matastructures disapear TOTALLY by analysing the published mRNA sequences of PFIZER and MODERNA vaccines. One fact is certain, the two mRNAs of the Moderna and Pfizer vaccines will result in a low functionality of the spike vaccine. This is because their designers by seeking greater stability, have doped to build CG rich sequences which, as soon as they are inserted into the human host, will, paradoxically, seek to mutate, like SARS-CoV2 variants, towards CG ==> UA forms in order to improve their STABILITY and LIFETIME. We conclude using new biomathematics theoretical methods (Master code and numerical standing waves), and comparing the Spikes of the two vaccines Moderna and Pfizer, that there will be very probable differences in stability and shelf life of the two respective mRNAs vaccines. However, “State of the Art” analyzes will disclose that their two protein sequences are strictly identical. By modified their synonymous codons using different strategies, no one can guarantee that the quantity of antibodies generated will be identical in the two cases. We wish to draw attention to the great ADAPTATION power - at the global scale of their genomes - of the most infectious VARIANTS, such as the BRAZIL 20J / 501Y.V3 variant (P.1). This is very worrying for the VACCINES <==> VARIANTS run: We demonstrate how the Brazilian variant P.1 which becomes uncontrollable in Brazil in April 2021 has a level of organization of long metastructures of 17,711 bases covering the genome which is 3.6 more important than that of the 2 reference genomes SARS-CoV2 and worldwide D614G. We suggest that this high level of overall structure of this variant contributes to the stability of this genome and, might explain its greater contagiousness.

Smith-Magenis syndrome is a complex neurobehavioral genetic disorder. The spectrum of SMS phenotype is broad but commonly includes craniofacial, neurobehavioral, and otolaryngologic features. While the etiology of SMS is commonly attributed to one copy interstitial deletion in the 17p11.2 region (90-95% of cases), variants identified by sequence analysis in RAI1 have also been reported in 5-10% of cases. The phenotypic spectrum of patients with RAI1 sequence alterations is not clear. In this study, we report a 9-year-old male with global cognitive and psychomotor developmental delay, musculoskeletal and cardiovascular abnormalities, and dysmorphic craniofacial features. Whole genome quad analysis of the proband, unaffected parent, and unaffected brother identified a novel de novo RAI1:c.2736delC variant. This is the first report of this variant in the literature. This report also highlights the details of the genome analysis and this patient's phenotypic spectrum.

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between modified p-Leonardo, p-Leonardo-Lucas, p-Leonardo numbers and Fibonacci, Lucas numbers.

The article features the structure and functions of plant synthetic promoters frequently exercised to precisely regulate complex regulatory routes. The composition of plant native promoters together with interacting proteins is presented to provide a better understanding of tasks associated with synthetic promoter development. The production of synthetic promoters is conferred on relatively small libraries produced generally by basic molecular or genetic engineering methods such as cis-element shuffling or domain swapping. Moreover, the preparation of large-scale libraries supported by synthetic DNA fragments, directed evolution, and machine or deep learning methodologies is presented. A particularly interesting group of synthetic promoters are bidirectional forms that enable the putative expression of up to 6–8 genes by one regulatory element. The introduction and controlled expression of several genes after one transgenic event strongly decreases the frequency of such problems as complex segregation patterns and random integration of multiple transgenes. These complications are commonly observed during transgenic crop development through traditional, multistep transformation by genetic constructs containing a single gene. Another path to solving problems associated with the low complexity and homology of already tested DNA fragments is through orthogonal expression systems composed of synthetic promoters and trans-factors that do not occur in nature or arise from different species. Their structure, functions, and applications are rendered in the article.

Abstract: The biological process of photosynthesis was critical in catalyzing the oxygenation of Earth’s atmosphere 2.5 billion years ago, changing the course of development of life on Earth. Recently, the fields of applied and synthetic photosynthesis have utilized the light-driven protein-pigment supercomplexes central to photosynthesis for the photocatalytic production of fuel and other various valuable products. The reaction center Photosystem I is of particular interest in applied photosynthesis due to its high stability post-purification, non-geopolitical limitation, and its ability to generate the greatest reducing power found in Nature. These remarkable properties have been harnessed for the photocatalytic production of a number of valuable products in the applied photosynthesis research field. These primarily include photocurrents and molecular hydrogen as fuels. The use of artificial reaction centers to generate substrates and reducing equivalents to drive non-photoactive enzymes for valuable product generation has been a long-standing area of interest of the synthetic photosynthesis research field. In this review, we cover advances in these areas and further speculate synthetic and applied photosynthesis as photocatalysts for the generation of valuable products.

Coronaviruses are a large family of RNA viruses which cause respiratory infections ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS), Severe Acute Respiratory Syndrome (SARS) and COVID-19. This article highlights some key findings based on a thorough scanning of genes of 475 SARS-CoV2 genomes, including the co-presence of ORF7a and ORF8 over the 256 SARS-CoV2 genomes and the absence of the gene ORF7b over the 219 SARS-CoV2 genomes collected from various countries including India. The presence of the gene ORF7b is found in the SARS-CoV2 genomes containing the L-type strain which is reported to having much higher virulence as compared to the S-type strain.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

The demographic history of anatomically modern humans (AMH) involves multiple migration events, population extinctions and genetic adaptations. As genome-wide data from complete genome sequencing becomes increasingly abundant and available even from extinct hominins, new insights of the evolutionary history of our species are discovered. It is currently known that AMH introgressed with archaic hominins once they left the African continent. Current out of African human genomes carry fragments of archaic origin. This review focuses on the fitness consequences of archaic interbreeding in current human populations. We discuss new insights and challenges that researchers face when interpreting the potential impact of introgression on fitness and testing hypotheses about the role of selection within the context of health and disease.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

Due to related uncertainties brought by changes in energy consumption and the integration of rooftop photovoltaic systems, the accuracy and availability of load profiling data are difficult to achieve. However, project managers and planners use a precise load profile as a crucial tool when determining whether the feeder must be updated or de-loaded. The paper aims to create a non-intrusive monitoring system that predicts the synthetic load profiles behavior of energy consumption using a Light Gradient Boosted and Support Vector Machine (SVM) machine learning technique. The most effective ML algorithm is chosen, and it has the potential to be assessed and verified using validation curves, residuals model generation, and prediction error metrics based on the following key statistical indicators: Mean Absolute Error, Mean Square Error, Root Mean Square Error, R-Square, Root Mean Squared Logarithmic Error, and Mean Absolute Percentage Error. The most effective ML has the potential to be assessed and verified using validation curves, residual model generation, and prediction error metrics based on the following key statistical indicators. The result shows that the estimation of the Irms avg -based on LightGBM is more accurate than the SVM because of its quick, economical, and difficult to overfit, particularly with high-dimensional data, speed, and efficiency of the MAE (3.0698), MSE (15.2757), RMSE (3.9020), RMSLE (0.1433), and MAPE (0.0049) respectively. Additionally, the machine learning model shows that, when compared to the SVM, the LightGBM model had the highest accurate prediction, with R-Square values of 89.8%, 90.3%, and 88.5% for Irms_A_avg, Irms_B_avg, and Irms_C_avg, respectively for Brakfontein Substation supply region, and best represents a diverse customer base.

Inflammatory bowel diseases (IBD) represent a growing public health concern due to increasing incidence worldwide. The current notion on the pathogenesis of IBD is that genetically susceptible individuals develop intolerance to dysregulated gut microflora (dysbiosis) and chronic inflammation develops as a result of environmental triggers. Among the environmental factors associated to IBD, diet plays an important role in modulating the gut microbiome, influencing epigenetic changes and, therefore, could be applied as a therapeutic tool to improve the disease course. Nevertheless, the current dietary recommendations for disease prevention and management are scarce and of weak evidence. This review summarizes the current knowledge on the complex interactions among diet, microbiome and epigenetics in IBD. Whereas over-abundance of calories and some macronutrients increases gut inflammation, several micronutrients have the potential to modulate it. Immunonutrition has emerged as a new concept putting forward the importance of vitamins such as vitamins A, C, E, D, folic acid and beta-carotene and trace elements such as zinc, selenium, manganese and iron. However, when assessed in clinical trials, specific micronutrients exerted a limited benefit. Beyond nutrients, anti-inflammatory dietary patterns as a complex intervention approach have become popular over the recent years. Hence, exclusive enteral nutrition in pediatric Crohn’s disease is the only nutritional intervention currently recommended as a first-line therapy. Other nutritional interventions or specific diets including the Specific Carbohydrate Diet, the low fermentable oligosaccharides, disaccharides, monosaccharides, and polyol diet and most recently the Mediterranean diet have shown strong anti-inflammatory properties and provide a promise for improving disease symptoms. Definitely, more work is required to evaluate the role of individual food compounds and complex nutritional interventions with potential to decrease inflammation as means for prevention and management of IBD.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

The risk classification of barrier lake is the key to conducting emergency treatment in a scientific manner. Such difficulties are faced as short time for risk evaluation, complex evaluation indicators, difficulty in obtaining information quickly and quantifying index weights. Based on this, this paper constructs a quantitative risk classification model for barrier lakes based on D-AHP. On the basis of studies on nearly 100 cases of barrier lakes, an 8-factor evaluation index system and quantitative classification are proposed. The methods of rapid calculation of reservoir capacity curve of barrier lake and intelligent identification of particles on the surface of barrier body were developed, which realized the rapid acquisition of 8-factor evaluation index information in emergency environment. The D-AHP method dealt with inconsistent weight assignment to evaluation factors by experts, which helped achieve weight quantification of 8 factors. The risk assessment on15 barrier lakes such as Tangjiashan barrier lake show that the conclusion drawn with risk classification method proposed in this paper is basically consistent with that of the traditional table-lookup method. However, the table-lookup method ignores cumulative loss’s impacts on the risk level of barrier lakes, and considers the extremely severe loss of barrier lakes as a sufficient condition for the evaluation level to be grade I, and thus a deviation in the evaluation. The risk classification method proposed in this paper is more reasonable and reliable.

In this work, we present a new way to study the genetic code mathematical and chemical structure, based on the use of mathematical computations involving some few recently designed Fibonacci-like sequences, the “seeds” (“initial conditions”) of which are chosen according to the chemical and physical data of the three amino acids serine, arginine and leucine, playing a prominent role in a recent symmetry classification scheme of the genetic code. It appears that these mathematical sequences, of the same kind as the famous Fibonacci series, apart from their usual recurrence relations, are highly interwinned by many useful linear relationships. Using these sequences and also various sums or linear combinations of them, we derive several physical and chemical quantities of interest, as the number of total coding codons, 61, obeying various degeneracy patterns, the detailed number of hydrogen atoms, the detailed number of atoms (H/CNOS) and the integer molecular mass (or nucleon number), in the side chains of the 61 “amino acids”, also in various degeneracy patterns, in agreement with those described in the literature. Also, unexpectedly but interestingly, we find, as a by-product, an accurate description of the very chemical structure of the four ribonucleotides uridine monophosphate (UMP), cytidine monophosphate (CMP), adenosine monophosphate (AMP) and guanosine monophosphate (GMP), the building blocks of RNA whose groupings, in three units, constitutes the triplet codons. In summary, we find a full mathematical and chemical connection with the “ideal sextet’s classification scheme” mentioned above as well as with several others, notably, the Findley-Findley-McGlynn symmetrical classification. We organize the content of the text in such a way that, besides the presentation of several new research results, it has also an educational dimension. The paper could therefore be read and the computations easily worked out, also by non-experts with mathematical background.

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

Considering the current needs of industry 4.0, especially in the condition of systems linked to artificial intelligence, this multidisciplinary concept work and difficult to execute, proposes the main idea of recognizing patterns using mathematical concepts of simple access and logical resolution of great potential. The objective of this work is to demonstrate a process for pattern recognition by applying the Fibonacci concept to vibration signals of hybrid dynamical systems. For this to be possible, it was necessary to use the concepts of preprocessing in a vector for pattern recognition, together with the concepts of the golden rule of Fibonacci, finally, all applied in the theorem of Jeffcott Rotors. The general result, from a technical point of view, demonstrates positivity and relationship of patterns, because, considering the aspect of the location between the values of the experimental and numerical result, both signs have similarities.

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

Historically the use of artificial intelligence (AI) in paediatrics dates back to 1984 with the intro-duction of a computer-assisted medical decision-making system called SHELP. Since then, research on the use of AI in pediatrics has become much more popular, and the number of reviewed publications largely increased. Consequently, a need for a holistic research landscape enabling researchers and other interested parties to gain insights into, deepen their knowledge about or inform them about the use of AI in pediatrics arised. To fill this gap a novel methodology named synthetic knowledge synthesis was applied. Using SKS we identified most prolific countries, in-stitutions, source titles, funding agencies, research themes, research gaps and hot spots.

The transformation of the state of polarization of a light beam by its linear interaction with a material medium can be modeled through the Stokes-Mueller formalism. The Mueller matrix associated with a given interaction depends on many aspects of the measurement configuration. In particular, different Mueller matrices can be measured for a fixed material sample depending on the spectral profile of the light probe. For a given light probe and a given sample with inhomogeneous spatial behavior, the polarimetric descriptors of the point-to-point Mueller matrices can be mapped leading to respective polarimetric images. The procedure can be repeated sequentially by using light probes with different central frequencies. In addition, the point-to-point Mueller matrices consecutively measured can be combined synthetically through convex sums leading to respective new Mueller matrices, in general with increased polarimetric randomness, thus exhibiting specific values for the associated polarimetric descriptors, including the indices of polarimetric purity, and generating new polarimetric images which are different from those obtained from the original Mueller matrices. In this work, the fundamentals for such synthetic generation of additional polarimetric images are described, providing a new tool that enhances the exploitation of Mueller polarimetry.

The number of people with neurodegenerative disease continues to increase every year. A new perspective is needed in overcoming this disease. In this review, researchers collected information about epigenetics and energy factors of neurodegenerative disease driven by mitochondria. Mitochondrial epigenetic dysregulation can cause damage to the neuron system. The increase in the amount and interaction of alpha-synuclein with SAMM50 in the mitochondria is one of the factors causing neurodegenerative disease. As an energy provider in the body, the existence of harmonization in the regulation of mitochondria specifically the mitochondrial outer membrane is important. Hydrogen peroxide (H₂O₂) has neuroprotective abilities to overcome the impairment function of mitochondria in neurodegenerative patients. Based on the computational simulation of this case, it can be used as the basic concept for the development of the role of H₂O₂ in neurodegenerative disease.

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

The reviews usefulness has been the aim of several research studies. However, results regarding the significance of usefulness determinants are often contradicting, thus decreasing the accuracy of reviews’ helpfulness estimation. Also, bias in user reviews attributed to differences e.g. in gender, nationality, etc., may result into misleading judgments thus diminishing reviews’ usefulness. Research is needed for sentiment analysis algorithms that incorporate bias embedded in reviews, thus improving their usefulness, readability, credibility, etc. This study utilizes fuzzy relations and fuzzy synthetic evaluation (FSE) in order to calculate reviews’ usefulness by incorporating users’ biases as expressed in terms of reviews’ articulacy and sentiment polarity. It selected and analysed 95.678 hotel user reviews from Tripadvisor, for five nationalities. The findings indicate that there are differences among nationalities. The British are most consistent in their judgments expressed in titles and review documents. The British and the Greek review titles suffice to convey any negative sentiments. The Dutch use fewer words in their reviews than the other nationalities. This study suggests that fuzzy logic captures subjectivity which is often found in reviews, and it can be used to quantify users’ behavioral differences, calculate reviews usefulness, and provide the means for developing more accurate voting systems.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis. Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$, $\gamma \approx 0.57721$ is the Euler-Mascheroni constant and $\log$ is the natural logarithm. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's criterion on superabundant numbers, we prove that the Riemann hypothesis is true.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

Diarrhea remains one of the leading causes of mortality worldwide, especially among children. Recent epidemiological studies conducted in developing countries identified Shigella species as the most predominant pathogenic bacteria responsible for diarrhea. Antimicrobial therapy is necessary for Shigella infections; however, the rapid emergence of resistance against existing antimicrobials in Shigella spp. poses a serious global health problem. To identify alternative antimicrobial compounds with activity against Shigella species, the pathogens responsible for bacterial diarrhea. In this study, we have applied antibacterial phenotypic screening to identify potent anti-Shigella compounds across a broad chemical diversity, including selected acetaminophen derivatives containing benzothiazoles backbone, and their combination with certain antibiotics. In continuation to our effort in searching potent antimicrobial compounds, we have found this time around that two acetaminophen derivatives containing benzothiazoles backbone (4a and 4b) could inhibit the growth of Shigella flexneri with common MIC value of 12.5 µg/ml. These compounds were established through a time-kill kinetics’ study to be bactericidal. Meanwhile, the 2-aminobenzothiazoles (1a and 1b) used for the synthesis of compounds 4 (a & b) were found to be poorly active (MIC: 100 µg/ml) against this pathogen. Combination studies of 4a and 4b with the least susceptible antibiotics (ceftriaxone and cotrimoxazole) demonstrated synergistic anti-Shigella activity. The present study demonstrates that the azobenzothiazole dyes 4 (a & b) can be repurposed as potential anti-Shigella compounds, which can serve as scaffolds for the development of new agents against infectious diarrhea caused by Shigella and other enteric pathogens, especially in developing countries.

In this study, we de novo assembled whole genomes of two small body-sized West Pacific sciaenids (Larimichthys polyactis and Collichthys lucidus) and compared them with published genome data of two closely-related, large body-sized species (Larimichthys crocea and Miichthys miiuy) and one distantly-related, large body-sized outgroup species (Dicentrarchus labrax). The phylogeny constructed using 7,403 single-copy orthologs shared among the five species indicated that L. crocea and L. polyactis diverged about 42 MYA. The two sibling taxa are more closely-related to C. lucidus than M. miiuy. We further identified four growth-related genes (CDHR2, PGC, PTN and PDGFA) that host five diagnostic amino acid variants on body size traits in the fishes, splitting small-body sized L. polyactis and C. lucidus from large-body sized L. crocea, M. miiuy and D. labrax. The results provide new genomic resources and guidelines to facilitate future endeavors in studying functional genomics and developing selective breeding programs for desirable growth traits in sciaenids.

The article presents the author's results of studying hidden rules of structural organizations of long DNA sequences in eukaryotic and prokaryotic genomes. The results concern some rules of percentages (or probabilities) of n-plets in genomes. To reveal such rules, the author considers genomic DNA nucleotide sequences as multilayers sequences of n-plets and studies the percentage contents of n-plets in different layers. Unexpected rules of invariance of total sums of percentages in certain tetra-groupings of n-plets in different layers of genomic DNA sequences are revealed. These discovered rules are candidates for the role of universal genomic rules. A tensor family of matrix representations of interrelated DNA-alphabets of 4 nucleotides, 16 doublets, 64 triplets, and 256 tetraplets is used in the study. This matrix approach allows revealing algebraic properties of the mentioned genetic rules of probabilities, which are useful for developing algebraic and quantum biology. Some analogies of the discovered genetic phenomena with phenomena of Gestalt psychology are noted and discussed. The author connects the received results about the genomic percentages rules with a supposition of P. Jordan, who is one of the creators of quantum mechanics and quantum biology, that life's missing laws are the rules of chance and probability of the quantum world. Additional attention is paid to the algebraic features of the system of structured DNA alphabets and their relationship with the methods of algebraic holography, known in the technique of processing discrete signals. The concept of algebraic-holographic genetics is being developed for the understanding of inherited holographic properties of organisms.

The ability to read and quantify nucleic acids such as DNA and RNA using sequencing technologies has revolutionized our understanding of life. With the emergence of synthetic biology, these tools are now being put to work in new ways - enabling de novo biological design. Here, we show how sequencing is supporting the creation of a new wave of biological parts and systems, as well as providing the vast data sets needed for the machine learning of design rules for predictive bioengineering. However, we believe this is only the tip of the iceberg and end by providing an outlook on recent advances that will likely broaden the role of sequencing in synthetic biology and its deployment in real-world environments.

Bone is a dynamic tissue with the capacity of repair and regeneration in specific conditions. Nevertheless, due to the increased incidence of bone disorders, the need of bone grafts has been growing over the past decades and the development of an ideal bone graft with optimal properties remains a clinical challenge. This review addresses the bone properties (morphology, composition and their repair and regeneration capacity) and puts the main focus on the potential strategies for developing bone repair and regeneration materials. It describes the requirements for designing a suitable scaffold material, types of materials (polymers, ceramics and composites) and techniques to obtain the porous structures (additive manufacturing techniques/robocasting or derived from marine skeletons) for bone tissue engineering applications. The main objective of this review is to gather the knowledge on the materials and methods for the production of scaffolds for bone tissue engineering and highlighting the potential of natural porous structures such as marine skeletons as promising alternative bone graft substitute materials without any further mineralogical changes, or after partial or total transformation into calcium phosphate. The suitability of the marine-derived porous bone graft substitutes for the intended applications will be also discussed.

In this paper, the distribution of prime numbers is expressed based on proving the Riemann hypothesis. The relationship between three numbers, three, six, and nine, and the modality to the distribution of prime numbers, is one of the results of Riemann's zeta function. Prime numbers are classified into six groups of single-digit numbers. There are no prime numbers in groups of three, six, and nine. The groups are made based on the sum of the internal digits. And for each set, there is an angle in the complex plane. The distance between the prime numbers in each group has a regular pattern. This pattern is a multiple of the numbers three, six, and nine. According to Euler's number, for an angle of 60 degrees, the real part of the cosine is 1/2. Accordingly, all prime numbers are related to angles greater than 60 degrees to 90 degrees. As a result, based on the relationship between the golden spiral and the complex conjugate of the zeta function, the function in The 1/2 point becomes zero based on the prime numbers.

MIMO (multiple-input multiple-output) radar provides much more flexibility than the traditional radar for its ability to realize far more observation channels than the actual number of T/R (transmit and receive) elements. Designing the array of MIMO imaging radar, the commonly used virtual array theory generally assumes that all elements are placed on the same line. However, due to the physical size of the antennas and coupling effect between T/R elements, a certain height difference between T/R arrays is essential, resulting in the defocusing of edge points of the scene. On the other hand, the virtual array theory implies far-field approximation, leading to inevitable high grating lobes in the imaging result of near-field edge points of the scene observed by common MIMO array. To tackle these problems, this paper derives the relationship between target’s PSF (point spread function) and pattern of T/R arrays, by which the design criterion of near-field imaging MIMO array is presented. Firstly, the proper height between T/R arrays is designed to focus the near-field edge points well. Secondly, the far-field array is modified to suppress the grating lobes in the near-field area. Finally, the validity of the proposed methods is verified by simulations and an experiment.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

The aim of this study was to evaluate the use of a flexible synthetic polymer bone graft to provide implant stability in the absence of implant stability during implant placement in a dense cortical bone model. Sockets were prepared on polyurethane blocks according to the standard implant socket drilling protocol in the control group, both oversizing and deepening in group 2, and oversizing only in group 3. In groups 2 and 3, flexible synthetic polymer bone grafts were placed in the sockets prior to implant placement. The implants were placed at bone level in all groups. The highest torque value obtained was recorded as the insertion torque. 75 implant sites in 3 groups were included in the study. The torque values of the implants in the control group were significantly higher than those of the implants with the oversized and deepened sockets and the oversized-only sockets (p&lt;0.05; p&lt;0.01).The torque values of the implants with the oversized and deepened sockets were significantly higher than those of the implants with the oversized-only sockets (p&lt;0.01). In this study, flexible synthetic polymer bone graft was shown to be effective in achieving implant stability in the management of implants with loss of primary stability.